Confidence Interval Calculator for Mean & Proportion

Calculate Your Confidence Interval

Select a calculation type and enter your sample statistics.

Private calculation

Sample mean

The arithmetic average calculated from your sample data.

Standard deviation

Enter the sample or known population standard deviation.

Sample size

The number of observations included in your sample.

Deviation type

Number of successes

The number of observations with the result of interest.

Sample size

The total number of people, items, or observations sampled.

Confidence level

The percentage of confidence intervals expected to contain the true value.

Apply finite population correction Use this when sampling without replacement from a known population.

Population size

The total number of members in the full population.

Please check your inputs.

Your Results

Awaiting data

Ready to calculate

Enter your sample information and click the calculate button to view a complete statistical breakdown.

Confidence interval

0 to 0

The estimated range for the true population value.

Interval range

0 Lower limit

0 Estimate

0 Upper limit

Margin of error 0

Standard error 0

Critical value 0

Confidence level 95%

Calculation method Mean interval

Point estimate 0

Sample size 0

Finite correction Not applied

Calculator features

Accurate Statistical Results Without Complex Software

This confidence interval calculator provides the important values needed to interpret sample estimates clearly.

Mean and Proportion Modes

Calculate an interval for a numerical sample mean or a percentage-based population proportion using the appropriate statistical method.

Flexible Confidence Levels

Select a common confidence level such as 90%, 95%, or 99%, or enter a custom confidence level for specialized analysis.

Complete Result Breakdown

Review the lower limit, upper limit, standard error, margin of error, critical value, sample size, and calculation method.

Simple process

How to Use the Confidence Interval Calculator

Complete your confidence interval calculation in three straightforward steps.

Select the Interval Type

Choose Sample Mean when estimating a numerical average. Choose Proportion when estimating a percentage, rate, or probability.

Enter Your Sample Data

Provide the requested sample mean, standard deviation, successes, sample size, confidence level, and optional population size.

Review the Calculated Range

Click Calculate Interval to see the estimated lower and upper limits, margin of error, standard error, and critical value.

What Is a Confidence Interval?

A confidence interval is a range of values used to estimate an unknown population parameter. Instead of reporting only one sample estimate, it provides a lower limit and an upper limit that reflect sampling uncertainty.

For example, suppose a survey estimates that 58% of customers are satisfied, with a 95% confidence interval from 48.3% to 67.7%. The interval indicates the range of plausible values for the true customer satisfaction rate based on the sample and calculation method.

Confidence Interval for a Mean

A confidence interval for a mean is commonly used for measurements such as income, height, test scores, delivery time, temperature, or product weight.

Confidence interval = Sample mean ± Critical value × Standard error

When the population standard deviation is known, the calculator uses a normal critical value. When only a sample standard deviation is available, it uses an approximate Student's t critical value based on the degrees of freedom.

Confidence Interval for a Proportion

A proportion interval is useful for yes-or-no outcomes, percentages, conversion rates, defect rates, approval ratings, and survey responses. This tool uses the Wilson score interval, which generally performs better than the basic Wald interval, especially for smaller samples or proportions close to zero or one.

How to Interpret the Results

A narrower interval indicates a more precise estimate.
A larger sample size usually produces a smaller margin of error.
A higher confidence level creates a wider interval.
Greater variability increases the standard error and interval width.
Finite population correction can reduce the margin of error when the sample represents a meaningful percentage of the population.

Common Confidence Levels

A 90% confidence level provides a narrower interval but less confidence. A 95% confidence level is widely used in research and business analysis. A 99% confidence level offers greater confidence but produces a wider range.

Frequently asked questions

Confidence Interval Calculator FAQs

Learn more about confidence levels, sample sizes, margins of error, and statistical interpretation.

A 95% confidence procedure means that if the same sampling process were repeated many times, approximately 95% of the calculated intervals would contain the true population parameter. It does not mean there is a 95% probability that a specific completed interval contains the parameter.

The margin of error is the distance between the point estimate and either end of the confidence interval. A result of 50 ± 3 has a margin of error of 3 and an interval from 47 to 53.

Use a z interval when the population standard deviation is known. Use a t interval when the standard deviation is estimated from the sample. The calculator automatically applies the appropriate method based on your deviation type selection.

Increasing the sample size generally lowers the standard error and produces a narrower confidence interval. Larger samples provide more precise estimates when the data quality and sampling method remain consistent.

A higher confidence level requires a larger critical value. That larger value increases the margin of error, creating a wider interval that provides greater confidence in the estimation procedure.

Finite population correction may be useful when sampling without replacement and the sample includes a substantial portion of the total population, commonly more than approximately 5% of the population.

No. A confidence interval estimates a population parameter such as a mean or proportion. A prediction interval estimates the likely range for an individual future observation and is normally wider.

Important: This calculator is intended for educational, research, and general analytical use. Results depend on the quality of the sample, the sampling method, and the assumptions of the selected statistical model.